What kind of sequence is this? 138, 123, 108, 93, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 138, 123, 108, 93, ... Are the consecutive differences in the sequence equal? 123 - 138 = -15, 108 - 123 = -15, 93 - 108 = -15. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.Check Geometric Possibility: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: 138, 123, 108, 93, ... Are the ratios between consecutive terms in the sequence equal? 123 / 138 ≈ 0.891, 108 / 123 ≈ 0.878, 93 / 108 ≈ 0.861. The ratios are not equal.Confirm Not Geometric: Since the ratios between consecutive terms are not equal, the sequence is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.

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What kind of sequence is this? $\newline$ $138, 123, 108, 93, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

138, 123, 108, 93, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: $138, 123, 108, 93, ext{...}$ Are the consecutive differences in the sequence equal? $123 - 138 = -15$ , $108 - 123 = -15$ , $93 - 108 = -15$ . The consecutive differences in the sequence are equal.
Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
Check Geometric Possibility: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: $138, 123, 108, 93, ext{...}$ Are the ratios between consecutive terms in the sequence equal? $123 / 138 hickapprox 0.891$ , $108 / 123 hickapprox 0.878$ , $93 / 108 hickapprox 0.861$ . The ratios are not equal.
Confirm Not Geometric: Since the ratios between consecutive terms are not equal, the sequence is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.